Geometry Chapter 2 Review Flashcards

Questions and Answers

What is inductive reasoning?

When several examples form a pattern and you assume the pattern will continue (correct)

A statement that can be written as 'If p, then q'

A process of using logic to draw conclusions from definitions

A method of proving theorems

What is a conjecture?

A statement that you believe to be true based on inductive reasoning

What is a counterexample?

A case in which a conjecture is not true

What is a conditional statement?

A statement written in the form if p, then q Signup and view all the answers

What is the hypothesis in a conditional statement?

The part p following the word if Signup and view all the answers

What is the conclusion in a conditional statement?

The part q following the word then Signup and view all the answers

What is the truth value of a conditional statement?

True (T) or false (F) Signup and view all the answers

If the hypothesis is true and the conclusion is true, then the conditional is true.

True Signup and view all the answers

If the hypothesis is true and the conditional is false, then the conditional is true.

False Signup and view all the answers

If the hypothesis is false, the conditional statement is true regardless of the conclusion.

True Signup and view all the answers

What is negation?

The opposite of a statement p written as ~p Signup and view all the answers

What is a converse?

The statement formed by exchanging the hypothesis and conclusion Signup and view all the answers

What is an inverse?

The statement formed by negating the hypothesis and conclusion Signup and view all the answers

What is a contrapositive?

The statement formed by negating and exchanging the hypothesis and conclusion Signup and view all the answers

What are logically equivalent statements?

Related conditional statements that have the same truth value Signup and view all the answers

What is deductive reasoning?

The process of using logic to draw conclusions from given facts, definitions, and properties Signup and view all the answers

What is the Law of Detachment?

If p → q is true and p is true, then q is true Signup and view all the answers

What is the Law of Syllogism?

If p → q and q → r are true, then p → r is also true Signup and view all the answers

What is a biconditional statement?

A statement that can be written in the form p if and only if q Signup and view all the answers

What is a proof?

An argument that uses logic, definitions, properties, and previously proven statements to show a conclusion is true Signup and view all the answers

What is the Addition Property of Equality?

If a = b, then a + c = b + c Signup and view all the answers

What is the Subtraction Property of Equality?

If a = b, then a - c = b - c Signup and view all the answers

What is the Multiplication Property of Equality?

If a = b, then ac = bc Signup and view all the answers

What is the Reflexive Property of Equality?

a = a Signup and view all the answers

What is the Symmetric Property of Equality?

If a = b, then b = a Signup and view all the answers

What is the Transitive Property of Equality?

If a = b and b = c, then a = c Signup and view all the answers

What is the Substitution Property of Equality?

If a = b, then b can be substituted for a (or vice versa) Signup and view all the answers

What is the Distributive Property?

a(b + c) = a * b + a * c Signup and view all the answers

What is the Reflexive Property of Congruence?

∠A ≅ ∠A Signup and view all the answers

What is the Transitive Property of Congruence?

If ∠1 ≅ ∠2 and ∠2 ≅ ∠3, then ∠1 ≅ ∠3 Signup and view all the answers

What is a theorem?

Any statement that you can prove Signup and view all the answers

What is the Linear Pair Theorem?

If two angles form a linear pair, then they are supplementary Signup and view all the answers

What is the Congruent Supplements Theorem?

If two angles are supplementary to the same angle, then the two angles are congruent Signup and view all the answers

What is a two-column proof?

A proof format that lists steps in one column and matching reasons in another Signup and view all the answers

What is the Right Angle Congruence Theorem?

All right angles are congruent Signup and view all the answers

What is the Congruent Complements Theorem?

If two angles are complementary to the same angle, then the two angles are congruent Signup and view all the answers

What is a flowchart proof?

A style of proof that uses boxes and arrows to show proof structure Signup and view all the answers

What is the Vertical Angles Theorem?

Vertical angles are congruent Signup and view all the answers

What does it mean if two congruent angles are supplementary?

Each angle is a right angle Signup and view all the answers

What is a paragraph proof?

A proof that presents steps and reasons as sentences in a paragraph Signup and view all the answers

Study Notes

Key Concepts in Geometry

Inductive Reasoning: A method that involves observing patterns through multiple examples and predicting future outcomes based on those patterns.
Conjecture: A belief or hypothesis that something is true based on inductive reasoning; can either be valid or invalid.
Counterexample: An instance that disproves a conjecture, demonstrating that it is not universally true.

Conditional Statements

Conditional Statement: Expressed as "if p, then q" (p → q), where p is the hypothesis and q is the conclusion.
Hypothesis (p): The condition in a conditional statement following "if."
Conclusion (q): The result or assertion following "then" in a conditional statement.
Truth Value: Indicates whether a conditional statement is true (T) or false (F).
True Conditional: Occurs when both the hypothesis and conclusion are true.
False Conditional: Occurs when the hypothesis is true but the conclusion is false.
Negation: Represents the opposite of a statement p, denoted as ~p.

Relationships and Conversions

Converse: Formed by swapping the hypothesis and conclusion (q → p).
Inverse: Created by negating both the hypothesis and conclusion (~p → ~q).
Contrapositive: Formed by both negating and swapping the hypothesis and conclusion (~q → ~p).
Logically Equivalent Statements: Related conditionals that share the same truth value.

Reasoning Methods

Deductive Reasoning: The process of drawing valid conclusions based on established facts, definitions, and logical properties.
Law of Detachment: If p → q is true and p is true, then q must also be true.
Law of Syllogism: If p → q and q → r are true, then p → r is likewise true.

Proofs and Properties

Biconditional Statement: A statement that asserts both conditions are equivalent, expressed as "p if and only if q."
Proof: A structured argument demonstrating the validity of a statement using logical reasoning, definitions, and previously established results.
Addition, Subtraction, Multiplication Properties of Equality: These properties illustrate how equal quantities can be manipulated similarly through basic arithmetic operations without changing their equality.
Reflexive, Symmetric, Transitive Properties of Equality:
- Reflexive: a = a
- Symmetric: If a = b, then b = a
- Transitive: If a = b and b = c, then a = c
Substitution Property: Allows for one variable to be replaced by another in an equation if they are equal.

Special Theorems

Distributive Property: a(b + c) = ab + ac; describes the distribution of multiplication over addition.
Linear Pair Theorem: States that two angles forming a linear pair are supplementary (sum to 180 degrees).
Congruent Supplements Theorem: States that two angles supplementary to the same angle are congruent to each other.
Congruent Complements Theorem: States that two angles complementary to the same angle are congruent.
Vertical Angles Theorem: Asserts that vertical angles are congruent.
Right Angle Congruence Theorem: All right angles are congruent.

Proof Styles

Two-Column Proof: Arranges statements and corresponding reasons in a structured two-column format.
Flowchart Proof: Utilizes boxes and arrows to visually represent proof structure.
Paragraph Proof: Presents the proof's steps and reasons in a cohesive narrative format.

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Description

This quiz covers key terms and concepts from Chapter 2 of Geometry. Terms include inductive reasoning, conjecture, counterexample, and conditional statements. Test your understanding with these flashcards designed to reinforce your knowledge of geometric principles.